Power — Question 10

Question 10

Energy capacity and power rating impose separate feasibility limits

A lifting drive has 9000 J of usable mechanical output energy and a maximum mechanical output power of 600 W. It must raise a 30 kg load by 20 m at a uniform speed during a 12 s cruise interval. Ignore startup and shutdown, take $g=10$ m/s$^2$, and neglect other losses.

1. Check whether the specified lift satisfies both limits.

2. Find the shortest allowed cruise time for the same rise.

3. Could a drive with 12000 J capacity but only 400 W output meet the original 12 s requirement?

Question 10 - Solution

Energy capacity and power rating impose separate feasibility limits

(a) Check energy and rate independently.

The governing relation is $$\boxed{E_{\mathrm{required}}=mgh,\qquad P_{\mathrm{required}}=\frac{mgh}{t}}$$ Required work is $$mgh=30(10)(20)=6000\ \mathrm J,$$ below 9000 J. Uniform required power is $$6000/12=500\ \mathrm W,$$ below 600 W. Both constraints are satisfied.

(b) Use the maximum power with the same work.

$$t_{\min}=6000/600=10\ \mathrm s$$ for the idealized cruise. Additional real startup or shutdown intervals are explicitly outside this model.

(c) More energy does not guarantee fast delivery.

The alternative has enough energy but requires at least $$6000/400=15\ \mathrm s.$$ It cannot meet 12 s; unused capacity cannot compensate for insufficient output power.